Uniqueness of stable capillary hypersurfaces in a ball

Abstract

In this paper we prove that any immersed stable capillary hypersurfaces in a ball in space forms are totally umbilical. This solves completely a long-standing open problem. In the proof one of crucial ingredients is a new Minkowski type formula. We also prove a Heintze-Karcher-Ros type inequality for hypersurfaces in a ball, which, together with the new Minkowski formula, yields a new proof of Alexandrov's Theorem for embedded CMC hypersurfaces in a ball with free boundary.

Final version, Math. Ann., to appear

References in corpus (1)

• Stability of capillary hypersurfaces in a Euclidean ball

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